Solve the differential equation + cos(x+ y)+2x]dx+[xe' +cos(x+ y)-1]dy = 0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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UNIVERSITY OF ANBAR
Ex. (13)
Solve the differential equation
[e + cos(x+ y)+2x]dx+[xe'+cos(x+ y)-1]dy=D0
Sol:-
Firs Stage: Check the equation is exact or not
OM
(e'+cos(x+ y)+ 2x)= e' - sin (x+
ôy ôy
ÔN
(xe' +cos(x+ y)-1) = e' sin
дх дх
انسو
حرمت
1) u, (x, y) = ƒM ( x, y) dx=[le' +cos(x+ y)+2x)dx
.. M, = N, equation is Exact
2) u, (x. y)= JN( x, §) dy = f(xe' +cos(x+ y)-1)dy
re + sin(x+ y)- y+ g(x)
3) u (x, ý) = xe" +sin(x+ y)+x -y=c
G.S
Page
Zevid T. Hbraheem
Transcribed Image Text:UNIVERSITY OF ANBAR Ex. (13) Solve the differential equation [e + cos(x+ y)+2x]dx+[xe'+cos(x+ y)-1]dy=D0 Sol:- Firs Stage: Check the equation is exact or not OM (e'+cos(x+ y)+ 2x)= e' - sin (x+ ôy ôy ÔN (xe' +cos(x+ y)-1) = e' sin дх дх انسو حرمت 1) u, (x, y) = ƒM ( x, y) dx=[le' +cos(x+ y)+2x)dx .. M, = N, equation is Exact 2) u, (x. y)= JN( x, §) dy = f(xe' +cos(x+ y)-1)dy re + sin(x+ y)- y+ g(x) 3) u (x, ý) = xe" +sin(x+ y)+x -y=c G.S Page Zevid T. Hbraheem
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